X^2+5x<24 interval notation

X²+5x-24<0

(x+8) (x-3) <0

treat the "<" sign as a "=" sign, you have x=-8, and x=3

take a number smaller than - 8, say - 9, plug x=-9 in to inequality to see if it works: (-9+8) is a negative, (-9-3) is a negative, the result is a positive, >0, so it doesn't work.

Next, take a number between - 8 and 3 and a number larger than 3 to try, you'll see that the answer is - 8